Existence of three solutions for Kirchhoff-type three-point boundary value problems

Abstract

The present paper is an attempt to investigate the multiplicity results of solutions for a three-point boundary value problem of Kirchhoff-type. Indeed, we will use variational methods for smooth functionals, defined on the reflexive Banach spaces in order to achieve the existence of at least three solutions for the equation. Finally, by presenting one example, we will ensure the applicability of our results.